Sure, I can help you identify and correct the mistakes in these sentences. Let's go through them one by one.

### Section 1

1. Although he is very young, Peter knows **to take** care of everything in his parents' absence.
- Correction: Although he is very young, Peter knows **how to take** care of everything in his parents' absence.

2. She always speaks English to her boss **meanwhile** she is in the office.
- Correction: She always speaks English to her boss **while** she is in the office.

3. When I came, Margaret, together with two other girls, **were** watering the flowers in the garden.
- Correction: When I came, Margaret, together with two other girls, **was** watering the flowers in the garden.

4. The coal is the world's **most** abundant fossil fuel.
- Correction: **Coal** is the world's most abundant fossil fuel.

5. Each year people around the world spend **billion** of dollars buying goods on the Internet.
- Correction: Each year people around the world spend **billions** of dollars buying goods on the Internet.

### Section 2

1. They asked me what **did happen** last night, but I was unable to tell them.
- Correction: They asked me what **happened** last night, but I was unable to tell them.

2. Air pollution, together with littering, **are** causing many problems in our industrial cities today.
- Correction: Air pollution, together with littering, **is** causing many problems in our industrial cities today.

3. These televisions are quite popular in Europe, but **those ones** are not.
- Correction: These televisions are quite popular in Europe, but **those** are not.

4. Nora **hardly never** misses an opportunity to play in the tennis tournaments.
- Correction: Nora **hardly ever** misses an opportunity to play in the tennis tournaments.

5. Many people believe that New York is the **most great** city in America.
- Correction: Many people believe that New York is the **greatest** city in America.

### Section 3

1. These televisions are very expensive for us to buy **at** this time, but perhaps we will return later.
- Correction: These televisions are very expensive for us to buy **at** this time, but perhaps we will return later.

2. Because they had spent too **many** time considering the new contract, the students lost the opportunity to lease the apartment.
- Correction: Because they had spent too **much** time considering the new contract, the students lost the opportunity to lease the apartment.

3. Buying clothes **are** often a very time-consuming practice because those clothes that a person likes are rarely the ones that fit him or her.
- Correction: Buying clothes **is** often a very time-consuming practice because those clothes that a person likes are rarely the ones that fit him or her.

4. John decided to buy a car **in** the morning, but in the afternoon he changed **his** mind.
- Correction: John decided to buy a car **in** the morning, but in the afternoon he changed **his** mind.

5. Jack always arrives **lately** for his chemistry class even though he leaves his dormitory in plenty of time.
- Correction: Jack always arrives **late** for his chemistry class even though he leaves his dormitory in plenty of time.

### Section 4

1. It is obvious that parents always protect their children **in dangers**.
- Correction: It is obvious that parents always protect their children **from danger**.

2. The wooden fence **surrounded** the factory is beginning to break due to the rain.
- Correction: The wooden fence **surrounding** the factory is beginning to break due to the rain.

3. Ann's new bicycle costs much more **than me**.
- Correction: Ann's new bicycle costs much more **than mine**.

4. When we go on vacation, we prefer swimming and active sports to sightseeing and **lie** on the beach.
- Correction: When we go on vacation, we prefer swimming and active sports to sightseeing and **lying** on the beach.

5. The harder he tried, the **worst** he danced before the large audience.
- Correction: The harder he tried, the **worse** he danced before the large audience.

I hope these corrections help! Let me know if you have any more questions.